This paper complements McCarthy's "The well designed child", in part by putting it in a broader context, the space of possible well designed progeny, and in part by relating design features to development of mathematical competence. I first moved into AI in an attempt to understand myself, especially hoping to understand how I could do mathematics. Over the ensuing four decades, my interactions with AI and other disciplines led to: design-based, cross-disciplinary investigations of requirements, especially those arising from interactions with a complex environment; a draft partial ontology for describing spaces of possible architectures, especially virtual machine architectures, for behaving systems (including our precursors); investigations of varied forms of representation and how they are suited to different functions; analysis of biological nature/nurture tradeoffs and their relevance to future machines; studies of control issues in a complex architecture; and showi...